ocaml: product except self

Author: PoorlyDefinedBehaviour

ocaml/product_except_self_dec_08_2023/main.ml

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+(*
+Given an integer array nums, return an array answer such that answer[i] is equal to the product of all the elements of nums except nums[i].
+
+The product of any prefix or suffix of nums is guaranteed to fit in a 32-bit integer.
+
+You must write an algorithm that runs in O(n) time and without using the division operation.
+
+Example 1:
+
+Input: nums = [1,2,3,4]
+Output: [24,12,8,6]
+Example 2:
+
+Input: nums = [-1,1,0,-3,3]
+Output: [0,0,9,0,0] 
+
+Constraints:
+
+2 <= nums.length <= 105
+-30 <= nums[i] <= 30
+The product of any prefix or suffix of nums is guaranteed to fit in a 32-bit integer.
+
+Follow up: Can you solve the problem in O(1) extra space complexity? (The output array does not count as extra space for space complexity analysis.)
+*)
+
+(*
+time O(n)
+space O(1)
+*)
+let product_except_self (nums : int array) : int array =
+  let nums_length = Array.length nums in
+
+  let suffix, _, _ =
+    Array.fold_right
+      (fun num (suffix, i, product) ->
+        suffix.(i) <- product;
+        (suffix, i - 1, product * num))
+      nums
+      (Array.make nums_length 0, nums_length - 1, 1)
+  in
+
+  let nums, _, _ =
+    Array.fold_left
+      (fun (nums, i, product) num ->
+        nums.(i) <- product * suffix.(i);
+        (nums, i + 1, product * num))
+      (nums, 0, 1) nums
+  in
+  nums
+
+(*
+time O(n)   
+space O(1)
+*)
+let product_except_self_2 (nums : int array) : int array =
+  let nums_length = Array.length nums in
+  let suffix = Array.make nums_length 0 in
+
+  let product = ref 1 in
+  for i = nums_length - 1 downto 0 do
+    suffix.(i) <- !product;
+    product := !product * nums.(i)
+  done;
+
+  let product = ref 1 in
+  for i = 0 to nums_length - 1 do
+    let num = nums.(i) in
+    nums.(i) <- !product * suffix.(i);
+    product := !product * num
+  done;
+
+  nums
+
+let () =
+  Printf.printf "v1: example 1: %b\n"
+    (product_except_self [| 1; 2; 3; 4 |] = [| 24; 12; 8; 6 |]);
+
+  Printf.printf "v1: example 2: %b\n"
+    (product_except_self [| -1; 1; 0; -3; 3 |] = [| 0; 0; 9; 0; 0 |]);
+
+  Printf.printf "v2: example 1: %b\n"
+    (product_except_self_2 [| 1; 2; 3; 4 |] = [| 24; 12; 8; 6 |]);
+
+  Printf.printf "v2: example 2: %b\n"
+    (product_except_self_2 [| -1; 1; 0; -3; 3 |] = [| 0; 0; 9; 0; 0 |])